TLC2933_13 Datasheet, PDF (15/24 Pages) Texas Instruments – HIGH-PERFORMANCE PHASE-LOCKED LOOP

TLC2933
HIGHĆPERFORMANCE PHASEĆLOCKED LOOP
SLAS136B − APRIL 1996 − REVISED JANUARY 2002
APPLICATION INFORMATION
Using the lag-lead filter in Figure 17(b) and divider N value, the transfer function for phase and frequency are
shown in equations 4 and 5. Note that the transfer function for phase differs from the transfer function for
frequency by only the divider N value. The difference arises from the fact that the feedback for phase is unity
while the feedback for frequency is 1/N.
Hence, the transfer function of Figure 17(a) for phase is
ȱ
ȳ
ȧ ȧ _F2(s)
ȧȧȲ _{ƪ ƫ ȴȧȧ F1(s)}
+
N
Kp _@
@ ^(T1
KV
) T2)
s2 ) s
1 ) s _@ T2
1
)
Kp_@KV _@T2
N_@(T1)T2)
)
Kp_@KV
N_@(T1)T2)
(4)
and the transfer function for frequency is
ȱ
ȳ
ȧ ȧ ^FOUT(s)
ȧȧȲ _{ƪ ƫ ȴȧȧ FREF(s)}
+
Kp
(T1
@ ^KV
) T2)
s2 ) s _@
1 ) s _@ T2
1
)
Kp_@KV_@T2
N_@(T1)T2)
)
Kp_@KV
N_@(T1)T2)
(5)
The standard 2-pole denominator is D = s² + 2 ζ ω_n s + ω_n2 and comparing the coefficients of the denominator
of equation (4) and (5) with the standard 2-pole denominator gives the following results.
Ǹ _{wn +}
Kp _@ KV
N _@ (T1 ) T2)
(6)
Solving for T1 + T2
T1
)
T2
+
Kp _@ KV
N @ w_n²
and by using this value for T1 + T2 in equation (6) the damping factor is
ǒ Ǔ z
+
w_n
2
@
T2
)
Kp
N
@
KV
(7)
solving for T2
T2
+
2z
w
–
Kp
N
@
KV
(8)
then by substituting for T2 in equation (6)
T1
+
KV _@ Kp
N @ w_n²
–
2z
w_n
)
N
Kp _@ KV
(9)
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